1102
Appendix VI.
the outer and inner diameters respectively of a ring of width b.
The Moment of Inertia of the ring will be found by deducting the
I of the cylinder r\ from that of the cylinder r0 : so from previous
reasoning,
I of ring - £(/o4-tf)
and, dividing by the weight
(rQ2 - r?)
MOMENTS OF INERTIA OF SOLIDS OF REVOLUTION.
'<st
TJU
I
Solid.
r*
r
= Wj X VOl.
inch Ib. units.
Cylinder
r 2
'0
r<>
wirJr0<
of radius r0
iv-pr^b
7.
^
2
Ring of radii -----
r* + r?
JJ+7?
w&b(r*-rF)
rQ outside
i* ( o » )
2
l~
2
n inside
The moment of inertia of any fly-wheel can now be calculated
by adding the moments of the separate parts; and the energy of
rotation is deduced by reference to equations (2) or (3).
Experimentally.—The Energy of Rotation may also be found
by direct experiment on the rotating solid. A fly-wheel A, Fig.
971, is fastened by a plate B to the ball-bearing hub c of a bi-
cycle, and is supported by the bracket D, held to the wall by
bolts. A small weight E is attached to a string wound round the
hub c, and serves by its fall to cause rotation of the fly-wheel.
Let the wheel be accurately balanced, so that it will rest equally
well ia any position, and let the frictional resistance of the ball-
bearing be quite inappreciable.
, The weight being w, the energy of the fall is wH foot pounds,